We assess the relative importance of spatial congestion and lowered temperature in the slowing dynamics of supercooled glycerol near the glass transition. We independently vary both volume, V , and temperature, T , by applying high pressure and monitor the dynamics by measuring the dielectric susceptibility. Our results demonstrate that both variables are control variables of comparable importance. However, a generalization of the concept of fragility of a glass-former shows that the dynamics are quantitatively more sensitive to fractional changes in V than T . We identify a connection between the fragility and a recently proposed density-temperature scaling which indicates that this conclusion holds for other liquids and polymers.PACS numbers: 64.70. Pf, 77.22.Gm When a liquid is cooled below its melting point its viscosity increases very rapidly with decreasing temperature until it turns into a glass, with solid-like properties. For instance, glycerol, a typical glass-former, shows a remarkable increase in viscosity and relaxation time of 14 orders of magnitude as it is cooled from 350K to 180K at 1 atmosphere [1]. There are two broad classes of explanations for this rapid increase of viscosity. One set of ideas identifies density as the crucial variable, arguing that the constraints on molecular rearrangements imposed by the dense packing in a liquid progressively increase due to the thermal contraction that accompanies cooling, until finally all motions are arrested in the glassy state. By this argument, the driving force for the rapid increase of viscosity in the case of glycerol would primarily be the 10% decrease in volume upon cooling. The second class of explanations for the slowing dynamics emphasizes the role of temperature: lowered temperature renders molecules too inactive to move around and surmount the energy barriers that impede exploration of their environment. In order to resolve the issue of whether it is temperature, T , or volume, V , that is the dominant variable in this phenomenon, experiments are required that independently control these variables. However, data of this kind are relatively sparse [2]. The objective of the experiments reported in this Letter is to distinguish unambiguously the effects of constrained volume and lowered temperature, by using high pressure as a mean of independently changing the density of the liquid.Glycerol is a widely-studied glass-former with broad industrial use. It is also an experimentally convenient sample: it has a high dielectric constant and does not easily crystallize. Moreover, some complementary high pressure data exist for glycerol [3,4,5,6]. These studies are principally isothermal experiments in which temperature is fixed and pressure is varied in discrete steps; as such, these data are not optimal for studying tempera- * Electronic address: win@physics.umass.edu † Electronic address: menon@physics.umass.edu ture dependence. They also appear to disagree with each other on the temperature dependence of the relaxation frequency ν p near the ...